Simple question what is the way to use bankers' rounding in BigQuery.
The only thing which I can find is:
BAD WAY to do it but still works:
CREATE TEMP FUNCTION test(num FLOAT64, decimalPlaces INT64)
RETURNS FLOAT64
LANGUAGE js AS """
var d = decimalPlaces || 0;
var m = Math.pow(10, d);
var n = +(d ? num * m : num).toFixed(8); // Avoid rounding errors
var i = Math.floor(n), f = n - i;
var e = 1e-8; // Allow for rounding errors in f
var r = (f > 0.5 - e && f < 0.5 + e) ?
((i % 2 == 0) ? i : i + 1) : Math.round(n);
return d ? r / m : r;
""";
SELECT ROUND(1.525,2)
There is a simpler way of calculating it:
CREATE TEMP FUNCTION bankersRound(num FLOAT64, decimals INT64)
RETURNS FLOAT64
LANGUAGE js AS """
var scale = Math.pow(10, decimals);
var result = value = (Math.round((num * scale) / 2) * 2) / scale;
return result;
""";
Bad way, but still works:
CREATE TEMP FUNCTION test(num FLOAT64, decimalPlaces INT64)
RETURNS FLOAT64
LANGUAGE js AS """
var d = decimalPlaces || 0;
var m = Math.pow(10, d);
var n = +(d ? num * m : num).toFixed(8); // Avoid rounding errors
var i = Math.floor(n), f = n - i;
var e = 1e-8; // Allow for rounding errors in f
var r = (f > 0.5 - e && f < 0.5 + e) ?
((i % 2 == 0) ? i : i + 1) : Math.round(n);
return d ? r / m : r;
""";
SELECT ROUND(1.525,2)
For a new project I like to calculate the moon phases. So far I haven't seen any code that does that. I don't want to rely on online-services for this.
I have tried some functions, but they are not 100% reliable. Functions I have tried:
NSInteger r = iYear % 100;
r %= 19;
if (r>9){ r -= 19;}
r = ((r * 11) % 30) + iMonth + iDay;
if (iMonth<3){r += 2;}
r -= ((iYear<2000) ? 4 : 8.3);
r = floor(r+0.5);
other one:
float n = floor(12.37 * (iYear -1900 + ((1.0 * iMonth - 0.5)/12.0)));
float RAD = 3.14159265/180.0;
float t = n / 1236.85;
float t2 = t * t;
float as = 359.2242 + 29.105356 * n;
float am = 306.0253 + 385.816918 * n + 0.010730 * t2;
float xtra = 0.75933 + 1.53058868 * n + ((1.178e-4) - (1.55e-7) * t) * t2;
xtra = xtra + (0.1734 - 3.93e-4 * t) * sin(RAD * as) - 0.4068 * sin(RAD * am);
float i = (xtra > 0.0 ? floor(xtra) : ceil(xtra - 1.0));
float j1 = [self julday:iYear iMonth:iMonth iDay:iDay];
float jd = (2415020 + 28 * n) + i;
jd = fmodf((j1-jd + 30), 30);
and last one
NSInteger thisJD = [self julday:iYear iMonth:iMonth iDay:iDay];
float degToRad = 3.14159265 / 180;
float K0, T, T2, T3, J0, F0, M0, M1, B1, oldJ = 0.0;
K0 = floor((iYear-1900)*12.3685);
T = (iYear-1899.5) / 100;
T2 = T*T; T3 = T*T*T;
J0 = 2415020 + 29*K0;
F0 = 0.0001178*T2 - 0.000000155*T3 + (0.75933 + 0.53058868*K0) - (0.000837*T + 0.000335*T2);
M0 = 360*[self getFrac:((K0*0.08084821133)) + 359.2242 - 0.0000333*T2 - 0.00000347*T3];
M1 = 360*[self getFrac:((K0*0.07171366128)) + 306.0253 + 0.0107306*T2 + 0.00001236*T3];
B1 = 360*[self getFrac:((K0*0.08519585128)) + 21.2964 - (0.0016528*T2) - (0.00000239*T3)];
NSInteger phase = 0;
NSInteger jday = 0;
while (jday < thisJD) {
float F = F0 + 1.530588*phase;
float M5 = (M0 + phase*29.10535608)*degToRad;
float M6 = (M1 + phase*385.81691806)*degToRad;
float B6 = (B1 + phase*390.67050646)*degToRad;
F -= 0.4068*sin(M6) + (0.1734 - 0.000393*T)*sin(M5);
F += 0.0161*sin(2*M6) + 0.0104*sin(2*B6);
F -= 0.0074*sin(M5 - M6) - 0.0051*sin(M5 + M6);
F += 0.0021*sin(2*M5) + 0.0010*sin(2*B6-M6);
F += 0.5 / 1440;
oldJ=jday;
jday = J0 + 28*phase + floor(F);
phase++;
}
float jd = fmodf((thisJD-oldJ), 30);
All are working more and less, but none is really giving the correct dates of full moon for 2017 and 2018.
Does anyone have a function that will calculate the moon phases correctly - also based on time zone?
EDIT:
I only want the function for the Moonphases. SwiftAA offers a lot more and only produces not needed overhead in the app.
I am planning to build an antenna tracker. I need to get bearing and tilt from GPS point A with altitude and GPS point B with altitude.
This is the example points:
latA = 39.099912
lonA = -94.581213
altA = 273.543
latB = 38.627089
lonB = -90.200203
altB = 1380.245
I've already got the formula for horizontal bearing and it gives me 97.89138167122422
This is the code:
function toRadian(num) {
return num * (Math.PI / 180);
}
function toDegree(num) {
return num * (180 / Math.PI);
}
function getHorizontalBearing(fromLat, fromLon, toLat, toLon) {
fromLat = toRadian(fromLat);
fromLon = toRadian(fromLon);
toLat = toRadian(toLat);
toLon = toRadian(toLon);
let dLon = toLon - fromLon;
let x = Math.tan(toLat / 2 + Math.PI / 4);
let y = Math.tan(fromLat / 2 + Math.PI / 4);
let dPhi = Math.log(x / y);
if (Math.abs(dLon) > Math.PI) {
if (dLon > 0.0) {
dLon = -(2 * Math.PI - dLon);
} else {
dLon = (2 * Math.PI + dLon);
}
}
return (toDegree(Math.atan2(dLon, dPhi)) + 360) % 360;
}
let n = getHorizontalBearing(39.099912, -94.581213, 38.627089, -90.200203);
console.info(n);
But I don't know how to find the tilt angle. Anyone could help me?
I think I got the answer after searching around.
This is the complete code, if you think this is wrong, feel free to correct me.
function toRadian(num) {
return num * (Math.PI / 180);
}
function toDegree(num) {
return num * (180 / Math.PI);
}
// North is 0 degree, South is 180 degree
function getHorizontalBearing(fromLat, fromLon, toLat, toLon, currentBearing) {
fromLat = toRadian(fromLat);
fromLon = toRadian(fromLon);
toLat = toRadian(toLat);
toLon = toRadian(toLon);
let dLon = toLon - fromLon;
let x = Math.tan(toLat / 2 + Math.PI / 4);
let y = Math.tan(fromLat / 2 + Math.PI / 4);
let dPhi = Math.log(x / y);
if (Math.abs(dLon) > Math.PI) {
if (dLon > 0.0) {
dLon = -(2 * Math.PI - dLon);
} else {
dLon = (2 * Math.PI + dLon);
}
}
let targetBearing = (toDegree(Math.atan2(dLon, dPhi)) + 360) % 360;
return targetBearing - currentBearing;
}
// Horizon is 0 degree, Up is 90 degree
function getVerticalBearing(fromLat, fromLon, fromAlt, toLat, toLon, toAlt, currentElevation) {
fromLat = toRadian(fromLat);
fromLon = toRadian(fromLon);
toLat = toRadian(toLat);
toLon = toRadian(toLon);
let fromECEF = getECEF(fromLat, fromLon, fromAlt);
let toECEF = getECEF(toLat, toLon, toAlt);
let deltaECEF = getDeltaECEF(fromECEF, toECEF);
let d = (fromECEF[0] * deltaECEF[0] + fromECEF[1] * deltaECEF[1] + fromECEF[2] * deltaECEF[2]);
let a = ((fromECEF[0] * fromECEF[0]) + (fromECEF[1] * fromECEF[1]) + (fromECEF[2] * fromECEF[2]));
let b = ((deltaECEF[0] * deltaECEF[0]) + (deltaECEF[2] * deltaECEF[2]) + (deltaECEF[2] * deltaECEF[2]));
let elevation = toDegree(Math.acos(d / Math.sqrt(a * b)));
elevation = 90 - elevation;
return elevation - currentElevation;
}
function getDeltaECEF(from, to) {
let X = to[0] - from[0];
let Y = to[1] - from[1];
let Z = to[2] - from[2];
return [X, Y, Z];
}
function getECEF(lat, lon, alt) {
let radius = 6378137;
let flatteningDenom = 298.257223563;
let flattening = 0.003352811;
let polarRadius = 6356752.312106893;
let asqr = radius * radius;
let bsqr = polarRadius * polarRadius;
let e = Math.sqrt((asqr-bsqr)/asqr);
// let eprime = Math.sqrt((asqr-bsqr)/bsqr);
let N = getN(radius, e, lat);
let ratio = (bsqr / asqr);
let X = (N + alt) * Math.cos(lat) * Math.cos(lon);
let Y = (N + alt) * Math.cos(lat) * Math.sin(lon);
let Z = (ratio * N + alt) * Math.sin(lat);
return [X, Y, Z];
}
function getN(a, e, latitude) {
let sinlatitude = Math.sin(latitude);
let denom = Math.sqrt(1 - e * e * sinlatitude * sinlatitude);
return a / denom;
}
let n = getHorizontalBearing(39.099912, -94.581213, 39.099912, -94.588032, 0.00);
console.info("Horizontal bearing:\t", n);
let m = getVerticalBearing(39.099912, -94.581213, 273.543, 39.099912, -94.588032, 873.543, 0.0);
console.info("Vertical bearing:\t", m);
Don Cross's javascript code produces good results. It takes into consideration the curvature of the earth plus the fact that the earth is oblate.
Example:
var elDegrees = calculateElevationAngleCosineKitty(
{latitude: 35.346257, longitude: -97.863801, altitudeMetres: 10},
{latitude: 34.450545, longitude: -96.500167, altitudeMetres: 9873}
);
console.log("El: " + elDegrees);
/***********************************
Code by Don Cross at cosinekitty.com
http://cosinekitty.com/compass.html
************************************/
function calculateElevationAngleCosineKitty(source, target)
{
var oblate = true;
var a = {'lat':source.latitude, 'lon':source.longitude, 'elv':source.altitudeMetres};
var b = {'lat':target.latitude, 'lon':target.longitude, 'elv':target.altitudeMetres};
var ap = LocationToPoint(a, oblate);
var bp = LocationToPoint(b, oblate);
var bma = NormalizeVectorDiff(bp, ap);
var elevation = 90.0 - (180.0 / Math.PI)*Math.acos(bma.x*ap.nx + bma.y*ap.ny + bma.z*ap.nz);
return elevation;
}
function NormalizeVectorDiff(b, a)
{
// Calculate norm(b-a), where norm divides a vector by its length to produce a unit vector.
var dx = b.x - a.x;
var dy = b.y - a.y;
var dz = b.z - a.z;
var dist2 = dx*dx + dy*dy + dz*dz;
if (dist2 == 0) {
return null;
}
var dist = Math.sqrt(dist2);
return { 'x':(dx/dist), 'y':(dy/dist), 'z':(dz/dist), 'radius':1.0 };
}
function EarthRadiusInMeters (latitudeRadians) // latitude is geodetic, i.e. that reported by GPS
{
// http://en.wikipedia.org/wiki/Earth_radius
var a = 6378137.0; // equatorial radius in meters
var b = 6356752.3; // polar radius in meters
var cos = Math.cos (latitudeRadians);
var sin = Math.sin (latitudeRadians);
var t1 = a * a * cos;
var t2 = b * b * sin;
var t3 = a * cos;
var t4 = b * sin;
return Math.sqrt ((t1*t1 + t2*t2) / (t3*t3 + t4*t4));
}
function GeocentricLatitude(lat)
{
// Convert geodetic latitude 'lat' to a geocentric latitude 'clat'.
// Geodetic latitude is the latitude as given by GPS.
// Geocentric latitude is the angle measured from center of Earth between a point and the equator.
// https://en.wikipedia.org/wiki/Latitude#Geocentric_latitude
var e2 = 0.00669437999014;
var clat = Math.atan((1.0 - e2) * Math.tan(lat));
return clat;
}
function LocationToPoint(c, oblate)
{
// Convert (lat, lon, elv) to (x, y, z).
var lat = c.lat * Math.PI / 180.0;
var lon = c.lon * Math.PI / 180.0;
var radius = oblate ? EarthRadiusInMeters(lat) : 6371009;
var clat = oblate ? GeocentricLatitude(lat) : lat;
var cosLon = Math.cos(lon);
var sinLon = Math.sin(lon);
var cosLat = Math.cos(clat);
var sinLat = Math.sin(clat);
var x = radius * cosLon * cosLat;
var y = radius * sinLon * cosLat;
var z = radius * sinLat;
// We used geocentric latitude to calculate (x,y,z) on the Earth's ellipsoid.
// Now we use geodetic latitude to calculate normal vector from the surface, to correct for elevation.
var cosGlat = Math.cos(lat);
var sinGlat = Math.sin(lat);
var nx = cosGlat * cosLon;
var ny = cosGlat * sinLon;
var nz = sinGlat;
x += c.elv * nx;
y += c.elv * ny;
z += c.elv * nz;
return {'x':x, 'y':y, 'z':z, 'radius':radius, 'nx':nx, 'ny':ny, 'nz':nz};
}
/***********************
END cosinekitty.com code
************************/
asking about speed or optimize the code
the kernel for sobel edge detection for gray img
When I run the program without any process only show input video and output(same as input) the frame per secounds fps=70 but when process down to 20 (process using GPU kernel for sobel)
Does anyone have an idea of how to speed up this code? I used local memory instead of global memory but the change is small.
How can I make all work items process the image?
sobel kernel
__kernel void hello_kernel(const __global uchar *input, __global uchar *output,const uint width,const uint height)
{
int x = get_global_id(0);
int y = get_global_id(1);
int index = width * y + x;
float a,b,c,d,e,f,g,h,i;
float8 v;
float sobelX = 0;
float sobelY = 0;
//if(index > width && index < (height*width)-width && (index % width-1) > 0 && (index % width-1) < width-1){
a = input[index-1-width] * -1.0f;
b =input[index-0-width] * 0.0f;
c = input[index+1-width] * +1.0f;
d = input[index-1] * -2.0f;
e = input[index-0] * 0.0f;
f = input[index+1] * +2.0f;
g = input[index-1+width] * -1.0f;
h = input[index-0+width] * 0.0f;
i = input[index+1+width] * +1.0f;
sobelX = a+b+c+d+e+f+g+h+i;
a = input[index-1-width] * -1.0f;
b = input[index-0-width] * -2.0f;
c = input[index+1-width] * -1.0f;
d = input[index-1] * 0.0f;
e = input[index-0] * 0.0f;
f = input[index+1] * 0.0f;
g = input[index-1+width] * +1.0f;
h = input[index-0+width] * +2.0f;
i = input[index+1+width] * +1.0f;
sobelY = a+b+c+d+e+f+g+h+i;
output[index] = sqrt(pow(sobelX,2) + pow(sobelY,2));
}
I'm trying to derive a CATransform3D that will map a quad with 4 corner points to another quad with 4 new corner points. I've spent a little bit of time researching this and it seems the steps involve converting the original Quad to a Square, and then converting that Square to the new Quad. My methods look like this (code borrowed from here):
- (CATransform3D)quadFromSquare_x0:(float)x0 y0:(float)y0 x1:(float)x1 y1:(float)y1 x2:(float)x2 y2:(float)y2 x3:(float)x3 y3:(float)y3 {
float dx1 = x1 - x2, dy1 = y1 - y2;
float dx2 = x3 - x2, dy2 = y3 - y2;
float sx = x0 - x1 + x2 - x3;
float sy = y0 - y1 + y2 - y3;
float g = (sx * dy2 - dx2 * sy) / (dx1 * dy2 - dx2 * dy1);
float h = (dx1 * sy - sx * dy1) / (dx1 * dy2 - dx2 * dy1);
float a = x1 - x0 + g * x1;
float b = x3 - x0 + h * x3;
float c = x0;
float d = y1 - y0 + g * y1;
float e = y3 - y0 + h * y3;
float f = y0;
CATransform3D mat;
mat.m11 = a;
mat.m12 = b;
mat.m13 = 0;
mat.m14 = c;
mat.m21 = d;
mat.m22 = e;
mat.m23 = 0;
mat.m24 = f;
mat.m31 = 0;
mat.m32 = 0;
mat.m33 = 1;
mat.m34 = 0;
mat.m41 = g;
mat.m42 = h;
mat.m43 = 0;
mat.m44 = 1;
return mat;
}
- (CATransform3D)squareFromQuad_x0:(float)x0 y0:(float)y0 x1:(float)x1 y1:(float)y1 x2:(float)x2 y2:(float)y2 x3:(float)x3 y3:(float)y3 {
CATransform3D mat = [self quadFromSquare_x0:x0 y0:y0 x1:x1 y1:y1 x2:x2 y2:y2 x3:x3 y3:y3];
// invert through adjoint
float a = mat.m11, d = mat.m21, /* ignore */ g = mat.m41;
float b = mat.m12, e = mat.m22, /* 3rd col*/ h = mat.m42;
/* ignore 3rd row */
float c = mat.m14, f = mat.m24;
float A = e - f * h;
float B = c * h - b;
float C = b * f - c * e;
float D = f * g - d;
float E = a - c * g;
float F = c * d - a * f;
float G = d * h - e * g;
float H = b * g - a * h;
float I = a * e - b * d;
// Probably unnecessary since 'I' is also scaled by the determinant,
// and 'I' scales the homogeneous coordinate, which, in turn,
// scales the X,Y coordinates.
// Determinant = a * (e - f * h) + b * (f * g - d) + c * (d * h - e * g);
float idet = 1.0f / (a * A + b * D + c * G);
mat.m11 = A * idet; mat.m21 = D * idet; mat.m31 = 0; mat.m41 = G * idet;
mat.m12 = B * idet; mat.m22 = E * idet; mat.m32 = 0; mat.m42 = H * idet;
mat.m13 = 0 ; mat.m23 = 0 ; mat.m33 = 1; mat.m43 = 0 ;
mat.m14 = C * idet; mat.m24 = F * idet; mat.m34 = 0; mat.m44 = I * idet;
return mat;
}
After calculating both matrices, multiplying them together, and assigning to the view in question, I end up with a transformed view, but it is wildly incorrect. In fact, it seems to be sheared like a parallelogram no matter what I do. What am I missing?
UPDATE 2/1/12
It seems the reason I'm running into issues may be that I need to accommodate for FOV and focal length into the model view matrix (which is the only matrix I can alter directly in Quartz.) I'm not having any luck finding documentation online on how to calculate the proper matrix, though.
I was able to achieve this by porting and combining the quad warping and homography code from these two URLs:
http://forum.openframeworks.cc/index.php/topic,509.30.html
http://forum.openframeworks.cc/index.php?topic=3121.15
UPDATE: I've open sourced a small class that does this: https://github.com/dominikhofmann/DHWarpView